Is it possible to use math commands in text without using $..$ or \(..\) as for example:
... testing \alpha more text
Is it possible to use math commands in text without using $..$ or \(..\) as for example:
... testing \alpha more text
While it's possible to coax LaTeX into allowing
... testing \alpha more text
or similar input, this opens the door to
... testing \alpha+\beta more text
or, even worse, to
... testing \alpha-\beta more text
which would give something we are, regrettably, used to see in poorly typeset documents. Getting trained into writing
\(\alpha\)
will help the typist to keep math properly segregated, so that TeX will be able to apply its special math processing.
If all you need is to type Greek words, as opposed to math symbols, the road is different: put
\usepackage[greek,english]{babel}
in your preamble. If you already use babel, add the greek option as the first one. Then
\textgreek{ABGDEZHJIKLMNXOPRSTUFQYW abgdezhjiklmnxoprstufqyw}
will typeset the Greek lowercase alphabet. The "tonos" can be input as a prefix apostrophe:
\textgreek{Ag'ia Sof'ia (Kwnstantino'upolh)}
will print Αγία Σοφία (Κωνσταντινούπολη)
There's also support for polytonic Greek.
All answers have mentioned using the alpha from the math font. If you are looking for typesetting a Greek word then you should use alpha from a text font. I don't know about LaTeX, but in ConTeXt there are two ways to use Greek letters from the text fonts. For both cases, you need to use a text font that has Greek letters (TeX Gyre Fonts have that, LM does not).
\setupbodyfont[palatino]
\starttext
\startTEXpage[width=6cm, offset=2mm]
There are two ways to get Greek letters in text mode:
\startitemize[n][headstyle=bold]
\head Type them directly
αβγδε \unknown
\head Use \type{\greek...} macros
\greekalpha\greekbeta\greekgamma\greekdelta\unknown
\stopitemize
Notice that text Greek symbols αβγδε differ from math Greek symbols $αβγδε$.
\stopTEXpage
\stoptext
which gives

You will need first to store the original commands using \let:
\let\storeAlpha=\alpha
and then redefine the command, here is a minimal:
\documentclass[10pt,a4paper]{article}
\usepackage{xspace}
\begin{document}
\let\storeAlpha=\alpha
\renewcommand\alpha{\relax\ifmmode{\storeAlpha}\else{$\storeAlpha$}\fi\xspace}
%% another way is to use \ensuremath
\let\storeBeta=\beta
\renewcommand\beta{\ensuremath{\beta}}
This is an \alpha and an $\alpha$ and an \(\alpha\) and a \beta.
\end{document}
The \ifmmode checks if TeX is in mathmode, if is true it will use the original command, otherwise the $..$ are inserted.
Sorry, but it is not possible to write math control sequences without placing them in a math environment such as $...$ Or $$...$$ or \[...\]. The only way I can see you doing this is by defining the control sequence you want using some of the several methods, but I will choose to use the ensuremath, to make sure that no matter what environment you are using your math commands in, the compiler will not complain to you and give you millions of errors.
Such as:
MWE:
\documentclass{article}
\def\alp{\ensuremath{\alpha} }
\begin{document}
This is a test that \alp works inside of the text-mode environment.
\end{document}
Which produces:

So this is one way to get the job done.
Hope this helped.
EDIT: As egreg kindly pointed out to me. The $$...$$ should not be used for display math instead use -> \[...\] as an "equivalent" (minus the spacing issues $$...$$ gives) alternative.